DuttonIndex#

class rojak.turbulence.diagnostic.DuttonIndex(u_wind: DataArray, v_wind: DataArray, geopotential: DataArray, use_dutton: bool = True)[source]#

Bases: Diagnostic

Dutton’s empirical index CAT diagnostic

Dutton’s empirical index [Dutton1980] was developed by performing multiple regression analysis on 11 synoptic-scale meteorological indices which have been previously identified as being predictors of CAT. It is defined as,

\[E = 1.25 S_{h} + 0.25 S_{v}^{2} + 10.5\]

where \(S_{v}\) is the vertical wind shear and \(S_{h}\) is the horizontal wind shear.

In Dutton’s paper, the horizontal wind shear is defined as,

(1)#\[S_{h} = \frac{1}{s^{2}} \left( uv \frac{ \partial u }{ \partial x } - u^{2} \frac{ \partial u }{ \partial y } + v^{2} \frac{ \partial v }{ \partial x } - uv \frac{ \partial v }{ \partial y } \right)\]

where \(s = \sqrt{ u^{2} + v ^{2} } = \left| \mathbf{v} \right|\) is the wind speed.

However, in the oft-cited [Sharman2006], it is defined with an additional factor of \(-1\),

(2)#\[S_{h} = \left( \frac{u}{s} \right) \frac{ \partial s }{ \partial y } - \left( \frac{v}{s} \right) \frac{ \partial s }{ \partial x }\]

The difference between Eq. (1) and Eq. (2) has resulted in an additional boolean kwarg (use_dutton) to control which definition of horizontal wind shear is used.

Parameters:

  • u_wind (DataArray) – Zonal wind speeds in m/s

  • v_wind (DataArray) – Meridional wind speeds in m/s

  • geopotential (DataArray) – Geopotential in m^2/s

  • use_dutton (bool) – Boolean to control which version of horizontal wind shear equation is used

__init__(u_wind: DataArray, v_wind: DataArray, geopotential: DataArray, use_dutton: bool = True) → None[source]#
Parameters:
Return type:

None

Methods

__init__(u_wind, v_wind, geopotential[, ...])

horizontal_wind_shear(speed)

Attributes

computed_value

name